Advanced Euclidean Geometry

Alfred S. Posamentier: Dean, City College of New York School of Education, 1999 - present; Professor of Mathematics Education, 1970 - present; Director, European Exchange Programs at the City College, (with Argentina, Austria, Czech Republic, Germany, Great Britain, Hungary, Poland) since 1983; Director, CCNY Extension Center at Rockland County Teacher's Center, since 1984.

• Preface. Introduction.About the Author.Chapter 1: Elementary Euclidean Geometry Revisited.Review of Basic Concepts of Geometry.Learning from Geometric Fallacies.Common Nomenclature.Chapter 2: Concurrency of Lines in a Triangle.Introduction.Ceva's Theorem.Applications of Ceva's Theorem.The Gergonne Point. Chapter 3: Collinearity of Points.Duality.Menelaus's Theorem.Applications of Menelaus's Theorem.Desargues's Theorem.Pascal's Theorem.Brianchon's Theorem.Pappus's Theorem.The Simson Line.Radical Axes.Chapter 4: Some Symmetric Points in a Triangle.Introduction.Equiangular Point.A Property of Equilateral Triangles.A Minimum Distance Point.Chapter 5: More Triangle Properties.Introduction.Angle Bisectors.Stewart's Theorem.Miquel's Theorem.Medians.Chapter 6: Quadrilaterals.Centers of a Quadrilateral.Cyclic Quadrilaterals.Ptolemy's Theorem.Applications of Ptolemy's Theorem.Chapter 7: Equicircles.Points of Tangency.Equiradii.Chapter 8: The Nine-Point Circle.Introduction to the Nine-Point Circle.Altitudes.The Nine-Point Circle Revisited.Chapter 9: Triangle Constructions.Introduction.Selected Constructions.Chapter 10: Circle Constructions.Introduction.The Problem of Apollonius.Chapter 11: The Golden Section and Fibonacci Numbers.The Golden Ratio.Fibonacci Numbers.Lucas Numbers.Fibonacci Numbers and Lucas Numbers in Geometry.The Golden Rectangle Revisited.The Golden Triangle.Index.